Hyperbolic 3-Manifolds with Boundary Which are Side-Pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-Sphere

Authors

  • Juan Pablo Díaz Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa. Cuernavaca, Morelos, México, 62209 https://orcid.org/0000-0001-7831-3152
  • Gabriela Hinojosa Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa. Cuernavaca, Morelos, México, 62209 https://orcid.org/0000-0003-2916-4634

DOI:

https://doi.org/10.37256/cm.5220242910

Keywords:

3-manifolds with boundary, link complement, knotted graph

Abstract

In this paper, we give a generalization of Ivanšić’s method for hyperbolic 3-manifolds without boundary, which allows us to recognize if a hyperbolic 3-manifold with totally geodesic boundary, given by an isometric sidepairing of two hyperbolic truncated tetrahedra, is the exterior of a knotted graph; i.e., it is the complement of a 1-manifold with isolated singularities embedded in 3,, in which case we get the corresponding diagram of the knotted isotopy class of its boundary. Otherwise, we obtain that the corresponding 3-manifold with boundary is the exterior of a knotted graph embedded in some lens space. Finally, we apply this method to a noncompact 3-manifold with a totally geodesic surface boundary of genus 2.

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Published

2024-04-26

How to Cite

1.
Díaz JP, Hinojosa G. Hyperbolic 3-Manifolds with Boundary Which are Side-Pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-Sphere. Contemp. Math. [Internet]. 2024 Apr. 26 [cited 2024 Jul. 3];5(2):1889-903. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2910